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Help with finding the sum of the infinite geometric series?

0 votes
1:

∑ 60 (1/10) ^k
k = 1

 2:

∑ 3.5^k
k = 1
asked May 3, 2013 in ALGEBRA 2 by linda Scholar

3 Answers

0 votes

1.

sum from k equal 1 to infinity of 60 open parentheses 1 over 10 close parentheses to the power of k equal 60 sum from k equal 1 to infinity of open parentheses 1 over 10 close parentheses to the power of k

space space space space space space space space space space space space space space space space space space space space equal 60 begin inline style open parentheses begin display style fraction numerator a over denominator 1 minus r end fraction end style close parentheses end style            (The sum of the infinite geometric series formula = fraction numerator a over denominator 1 minus r end fraction where open vertical bar r close vertical bar less than 1)   

space space space space space space space space space space space space space space space space space space space space equal 60 begin inline style open parentheses begin display style fraction numerator begin display style 1 over 10 end style over denominator 1 minus begin display style 1 over 10 end style end fraction end style close parentheses end style       (Substitute a equal 1 over 10 and r equal 1 over 10 in the above formula)

space space space space space space space space space space space space space space space space space space space space equal 60 begin inline style open parentheses begin display style fraction numerator begin display style 1 over 10 end style over denominator begin display style 9 over 10 end style end fraction end style close parentheses end style             (Simplify)

space space space space space space space space space space space space space space space space space space space space equal 60 begin inline style open parentheses begin display style 1 over 9 end style close parentheses end style

space space space space space space space space space space space space space space space space space space space space equal 20 over 3.

 

answered May 3, 2013 by diane Scholar
0 votes

2.

sum from k equal 1 to infinity of open parentheses 3.5 close parentheses to the power of k equal sum from k equal 1 to infinity of open parentheses 7 over 2 close parentheses to the power of k

space space space space space space space space space space space space space space space space space space space space equal begin inline style open parentheses begin display style fraction numerator a over denominator r minus 1 end fraction end style close parentheses end style            (The sum of the infinite geometric series formula = fraction numerator a over denominator r minus 1 end fraction where open vertical bar r close vertical bar greater than 1)   

space space space space space space space space space space space space space space space space space space space space equal begin inline style open parentheses begin display style fraction numerator begin display style 7 over 2 end style over denominator begin display style 7 over 2 end style minus 1 end fraction end style close parentheses end style       (Substitute a equal 7 over 2 and r equal 7 over 2 in the above formula)

space space space space space space space space space space space space space space space space space space space space equal begin inline style open parentheses begin display style fraction numerator begin display style 7 over 2 end style over denominator begin display style 5 over 2 end style end fraction end style close parentheses end style             (Simplify)

space space space space space space space space space space space space space space space space space space space space equal begin inline style open parentheses begin display style 7 over 2 end style close parentheses end style open parentheses 2 over 5 close parentheses

space space space space space space space space space space space space space space space space space space space space equal 7 over 5.

 

answered May 3, 2013 by diane Scholar
0 votes

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Sum of infinite sequence is image

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answered Jul 14, 2014 by david Expert

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